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I'm working through revision questions at the moment and we are asked to compute the price of an American call option.

Suppose that $dS_t = \sigma S_t dW^*_t, S_0 >0$

Let $0<U<T$ be fixed dates and let $K>0$ be a constant. Consider the American call option with expiration date $T$ and payoff process $(X_t)_{t\in[0,T]}$ given by the following expressions:

$X_t = g_1(S_t,t) = (S_t-K)^+ , \forall t \in [0,U]$

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$X_t = g_2(S_t,t) = (S_t-S_U)^+ , \forall t \in (U,T]$

Find the arbitrage price of the option at time $t\in [0,T]$

We know that in time $t \in (U,T]$ the price is a European call with strike $S_U$, and the price at time $U$ is max$(C_u(K), C_u(S_u))$ (I think).

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closed as unclear what you're asking by SRKX Jun 18 '15 at 4:33

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ "Analyze the price" is too vague to be answered properly here. What are you looking to express? Please rephrased you title as a question and make it specific in the description; we will then reopen the question. $\endgroup$ – SRKX Jun 18 '15 at 4:33